The volume \( V \) of a right circular cylinder is given by \( V=\pi r^{2} h \), where \( r \) is the radius and \( h \) is the heigh If \( h \) is held fixed at \( h=9 \) inches, find the rate of change of \( V \) with respect to \( r \) when \( r=3 \) inches. The rate is \( \square \mathrm{in}^{2} \). (Type an exact answer in terms of \( \pi \).)

3. (15б) Найдите полный дифференциал и полное приращение функции \( z=\sqrt{x y^{2}-y^{3}} \) точке \( A(2,1) \) при \( \Delta x=0,1 \) и \( \Delta y=0,2 \).

\( \lim _ { n \rightarrow \infty } \frac { 5 ^ { n } \cdot n ! } { n ^ { n } } = \)

7. (15б) Выясните, является ли функция \( z=\ln \left(x^{2}+y^{2}+2 y+1\right) \) решением уравнения \( \frac{\partial^{2} z}{\partial x^{2}}+\frac{\partial^{2} z}{\partial y^{2}}=0 \)

f \( y=\frac{1+x}{1-x} \), find \( \frac{d y}{d x} \)

Change the order of integration in \( \int_{0}^{a} \int_{x}^{a}\left(x^{2}+y^{2}\right) d y d x \) and hence evaluate it. (OR)